Modelling collective animal behaviour David J. T. Sumpter Department of Mathematics Uppsala University
Moving together Aggregation in space. Moving in the same direction. Complex patterns.
Self-propelled particle models current positioncurrent velocity position and velocity of neighbours stochastic effect future position future velocity
Aggregation model in one dimension current positioncurrent velocity position and velocity of neighbours stochastic effect future position future velocity e is a random number selected uniformly at random from a range
Aggregation model in one dimension
Cockroach aggregation Cockroaches Model
Radakov’s fish
Alignment model in one dimension current positioncurrent velocity position and velocity of neighbours stochastic effect future position future velocity e is a random number selected uniformly at random from a range
Position: Velocity: Time SpaceTime Average direction Alignment model in one dimension
Position: Velocity: Time SpaceTime Average direction Alignment model in one dimension
Position: Velocity: Time SpaceTime Average direction Alignment model in one dimension
Transition from disorder to order measures order in the system. η is degree of randomness, ρ is density (number of particles over size of world).
Transition from disorder to order measures order in the system. η is degree of randomness, ρ is density (number of particles over size of world).
Transition from disorder to order measures order in the system. η is degree of randomness, ρ is density (number of particles over size of world).
Alignment model in two dimensions current positioncurrent velocity position and velocity of neighbours stochastic effect future position future velocity where the θ j are the directions of i’s neighbours and ε is chosen uniformly at random from a range.
Alignment model in two dimensions
Attraction, alignment and repulsion in three dimensions
Collective Animal Behaviour
Collective Animal Behaviour
Collective Animal Behaviour
Collective Animal Behaviour
Collective Animal Behaviour